The $L_p$ Minkowski problem for the electrostatic $\mathfrak{p}$-capacity

Abstract

Existence and uniqueness of the solution to the $L_p$ Minkowski problem for the electrostatic $\mathfrak{p}$-capacity are proved when $p \gt 1$ and $1 \lt \mathfrak{p} \lt n$. These results are nonlinear extensions of the very recent solution to the $L_p$ Minkowski problem for $\mathfrak{p}$-capacity when $p = 1$ and $1 \lt \mathfrak{p} \lt n$ by Colesanti et al. and Akman et al., and the classical solution to the Minkowski problem for electrostatic capacity when $p = 1$ and $\mathfrak{p} = 2$ by Jerison.